Work on Linear Quadratic and Cubic Functions

  Work on Linear Quadratic and Cubic Functions  

x^3 + y^3 = (x + y) (x^2 - xy + y^2)

implies x^2 - xy + y^2 = 5

Now 3(x-y)^2 + (x+y)^2 = 4(x^2 - xy + y^2)

So 3(x-y)^2 = 16

Lastly, x^2 + y^2 = (1/2)[(x+y)^2 + (x-y)^2]

= (1/2)(2^2 + 16/3) = 14/3

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